Need Help with "Exact Values" and absolute value of a linear function.

**liveboon** · August 30th 2010, 08:05 PM

1. Don't understand how exact values work
2. |3x-2| = 4 ---- Please solve

**mathaddict** · August 30th 2010, 08:28 PM

Originally Posted by liveboon

1. Don't understand how exact values work
2. |3x-2| = 4 ---- Please solve

(1) If the question asks for the exact value of $\frac{2}{\sqrt{2}}$ , you are expected to give the answer in surd form, $\sqrt{2}$ instead of 1.41 because $\sqrt{2}$ is the more exact value to represent the answer than 1.41

(2) $3x-2=\pm 4$

**Prove It** · August 31st 2010, 12:32 AM

2.
$|3x - 2| = 4$

Remember that $|3x - 2| = \begin{cases}\phantom{-(}3x-2\phantom{)}\,\textrm{if }3x - 2 \geq 0\\ -(3x - 2)\,\textrm{if }3x - 2 < 0\end{cases}$

$= \begin{cases}3x - 2 \,\textrm{if } x \geq \frac{2}{3}\\ 2 - 3x \,\textrm{if }x < \frac{2}{3}\end{cases}$

So IF $3x - 2 = 4$ then $x = 2$ . Is this possible?

IF $2 - 3x = 4$ then $x = -\frac{2}{3}$ . Is this possible?

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